Suppose the half-life is 9.0 s for a first order reaction and the reactant concentration is 0.0741 M 50.7 s after the reaction starts. How many seconds after the start of the reaction does it take for the reactant concentration to decrease to 0.0055 M?

The time taken by the reaction is 84.5 seconds

Explanation:

The equation used to calculate half life for first order kinetics:

where,

= half-life of the reaction = 9.0 s

k = rate constant = ?

Putting values in above equation, we get:

Rate law expression for first order kinetics is given by the equation:

    ......(1)

where,

k = rate constant  =

t = time taken for decay process = 50.7 sec

= initial amount of the reactant = ?

[A] = amount left after decay process =  0.0741 M

Putting values in equation 1, we get:

Now, calculating the time taken by using equation 1:

Putting values in equation 1, we get:

Hence, the time taken by the reaction is 84.5 seconds

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